Abstract

In binary regression, modelling imbalanced data pose various challenges on statistical methods and algorithms, potentially leading to a biased estimation in the majority class of zeros
(or ones) and generate a flawed conclusion in the minority class of zeros (or ones). Though,
the data from the majority class is vital, but child illness and death are analyzed and sampled through the minority class (that is, children ≤ 60 months that are either dead or sick).
From the Bayesian perspective, several link functions (symmetric and asymmetric model)
have been proposed to improve the performance of the minority class of an imbalanced data.
This imbalanced data encapsulating spatial characteristics collected at different points and
geographically influenced the specific locations observed based on the information gathered.
Four link functions, known as baseline including logit, probit, cloglog and loglog models were
compared for Bayesian optimal models and variable selection. The probit model was chosen due to its lowest value of deviance and strong performance across copious information
criteria. Thus, the study developed a Bayesian Gaussian copula model using a recursive
bivariate probit approach applied to child death and illness, an onus in the emerging world,
particularly in sub-Saharan Africa countries. With the aim that child illness and other sociodemographic characteristics can contribute to death, the study seeks to bridge this void by
exploring the cynosure between the prevalence of child illness and death in Nigeria, taking
into account the spatial factors, thereby contributing to a more comprehensive understanding of this issue. We utilized a two-stage dataset obtained from the Nigeria demographic and
Health survey for the year 2008, 2013, and 2018 at the interval of 5 consecutive years. A total of 94, 053 observations were gathered across the 36 states plus Federal capital Territory,
Abuja, Nigeria but only 41, 168 were used after the proper data management techniques.
For instance, the dataset on child illness and death recorded that any child who has either
a fever, cough or diarrhoea in the last 2 weeks was coded as 1 and otherwise as 0. Similarly, any child whose death occurred during infancy, perinatal, neonatal, and < 5 death
are recategorized as 1 and 0 otherwise. The Bayesian Gaussian copula with recursive bivariate probit model was implemented on rstan. We introduced a Gaussian Markov Random
Field (iCAR) spatial prior to model the variability and spatial pattern of the model and
∗Email: oluwafunmilayo@usp.br.
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considered a weakly informative prior (Gaussian prior) for the model parameters. Thus, the
study discovered that two of the socio-demographic characteristics are significant with child
mortality and morbidity. The findings from the spatial pattern revealed a slight difference
across the 37 states. Only children living in Katsina state showed a consistent lower risk of
the individual and the joint effect of illness and death.